Presently, in order to shorten a charging time when a rechargeable battery, a simplest method is to increase a charging current/rate. However, this kind of methods will accelerate aging speed of the rechargeable battery, which results in reducing fully charged capacity (FCC) of the rechargeable battery, increasing the internal resistance and unsatisfying the warranty life. The so-called FCC of the rechargeable battery means that the capacity when battery is fully charged. In general, the battery aging phenomenon includes the capacity degradation and internal resistance increase. To decelerate the aging speed of the rechargeable battery, a general method is to preload a setting table of battery temperatures vs. charging currents, battery temperatures vs. battery charging voltages or the likes when charging the battery. For example, the charging current can be calculated by using current status. However, the error of this kind of look-up table methods will increase when battery is aging and its characteristic has been changed. In addition, such methods are still unable to attain the balance between the charging time and the warranty life. Therefore, it is an important issue in this field to find the optimal solution between the battery lifespan and quick charging time.